286 



SCIENCE 



[N. S. Vol. XXX. No. 765 



dissonant chords, those in which such inter- 

 vals occur. This definition, it may be added, 

 has been in use in the writer's classes for 

 several years, with satisfactory results. 



Objection to this position was recently made, 

 on the ground that, in our experience, there is 

 not so clear a discrimination, as is implied, 

 between seconds and sevenths, on the one 

 hand, and all the remaining intervals, on the 

 other. Specifically, the claim was advanced 

 that the interval of an augmented fourth, 

 traditionally known as a dissonance, sounds 

 equally harsh with the seconds and the 

 sevenths. 



In order to test the truth of these opposite 

 opinions, the writer recently decided to con- 

 duct an experiment in which the reactions to 

 various intervals might be determined in the 

 case of persons who, though untrained in 

 musical theory, are yet sensitive to musical 

 effects. A collegiate class was selected for the 

 experiment, a class of music-lovers ignorant of 

 the technique of musical structure. 



In order that the validity of the tests might 

 not be affected by any preconceived notions 

 on the part of the performer, the playing of 

 the various intervals employed was entrusted 

 to an assistant, who was kept in total ignor- 

 ance of the nature and purpose of the experi- 

 ment. The intervals were played on a grand 

 pianoforte of good quality, and the assistant 

 was instructed, as far as possible, to employ 

 the same touch and intensity throughout the 

 tests. Each interval was played from a manu- 

 script copy; and, after a pause of perhaps two 

 seconds, repeated. Before the following in- 

 terval was performed, ten seconds, approxi- 

 mately, were allowed to elapse, during which 

 the number of the coming test was announced ; 

 it was hoped that, in this way, the various 

 combinations would be isolated. The order 

 of presentation had been previously deter- 

 mined, by lot. Every care was exercised to 

 make the experiment scientifically accurate; 

 so that the results, it is believed, are, in every 

 way, trustworthy. 



The following explanation was written on 

 the blackboard before the class : " Assume that 

 all musical intervals (an interval is a com- 



bination of two simultaneous tones differing, 

 more or less, in pitch) can be classified in two 

 groups, which we shall call Group X and 

 Group Y. Let Group X include intervals 

 whose sound is smooth; let Group Y include 

 intervals whose sound is harsh. Three inter- 

 vals will now be played representing Group 

 X; and afterward three intervals representing 

 Group Y." At this point the assistant was 

 called from an adjoining room, and requested 

 to play the following intervals representing 

 Group X : a major third, a major sixth and a 

 minor third. Afterward, he was requested 

 to play the following intervals representing 

 Group Y: a major seventh, a major second 

 and a minor second. 



The actual tests were then presented to the 

 class. These consisted of a series of twenty- 

 two intervals, in which each combination from 

 a minor second to a major seventh was in- 

 cluded twice. The students were requested to 

 record, in writing, the name of the group (X 

 or Y) to which, in their judgment, each in- 

 terval belonged. 



Thirty-five students replied, affording sev- 

 enty tests in the case of each interval. The 

 results are collated in the following table: 



Smooth Harsh 



Minor second 70 



Major second 5 65 



Minor third 67 3 



Major third 68 2 



Perfect fourth 56 14 



Augmented fourth 68 2 



Perfect fifth 53 17 



Minor sixth 68 2 



Major sixth 69 1 



Minor seventh 4 66 



Major seventh 2 68 



The significant features of the replies are: 



1. The almost unanimous verdict that sec- 

 onds and sevenths are harsh, whereas aU other 

 intervals are "smooth. 



2. The large number of dissenters from the 

 prevailing opinion that perfect fourths and 

 perfect fifths are smooth. 



3. The almost unanimous verdict that the 

 augmented fourth (the same, on the piano- 

 forte, as the diminished fifth) is smooth — just 

 as smooth as the thirds and sixths, and much 



